A Linearized High-Order Combined Compact Difference Scheme for Multi-Dimensional Coupled Burgers' Equations

作者：Chen, Buyun; He, Dongdong^*; Pan, Kejia

来源：Numerical Mathematics: Theory, Methods and Applications , 2018, 11(2): 299-320.

DOI：10.4208/nmtma.OA-2017-0090

• Combined compact difference scheme
• coupled Burgers' equations
• linearized method
• ADI method
• unconditional stability

Multi-dimensional coupled Burgers' equations are important nonlinear partial differential equations arising in fluid mechanics. Developing high-order and efficient numerical methods for solving the Burgers' equation is essential in many real applications since exact solutions can not be obtained generally. In this paper, we seek a high-order accurate and efficient numerical method for solving multi-dimensional coupled Burgers' equations. A linearized combined compact difference (CCD) method together with alternating direction implicit (ADI) method is proposed. The CCD-ADI method is sixth-order accuracy in space variable and second-order accuracy in time variable. The resulting linear system at each ADI computation step corresponds to a block-tridiagonal system which can be effectively solved by the block Thomas algorithm. Fourier analysis shows that the method is unconditionally stable. Numerical experiments including both two-dimensional and three-dimensional problems are conducted to demonstrate the accuracy and efficiency of the method.

• 出版日期2018-5
• 单位香港中文大学（深圳）; 中南大学; 同济大学